Particle with spin S=3/2 in Riemannian space-time

2011/09/18 by Red'kov, V. M.
#35 #FOS: Physical sciences #G.1 #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1109.3871

Abstract

Equations for 16-component vector-bispinor field, originated from Rarita-Schwinger Lagrangian for spin 3/2 field extended to Riemannian space-time are investigated. Additional general covariant constrains for the field are produced, which for some space-time models greatly simplify original wave equation. Peculiarities in description of the massless spin 3/2 field are specified. In the flat Minkowski space for massless case there exist gauge invariance of the main wave equation, which reduces to possibility to produce a whole class of trivial solutions in the the form of 4-gradient of arbitrary (gauge) bispinor function, Ψ⁰_c = ∂_c ψ. Generalization of that property for Riemannian model is performed; it is shown that in general covariant case solutions of the gradient type Ψ⁰_β = (∇_β + Γ_β)Ψexist in space-time regions where the Ricci tensor obeys an identity R_αβ - 1 \over 2 R g_αβ = 0.

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